##### Hamming, Richard W.

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.

In N. Rose Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.

##### Hamilton, Sir William Rowan (1805-1865)

On earth there is nothing great but man; in man there is nothing great but mind.

##### Hamilton, Sir William Rowan (1805-1865)

I regard it as an
inelegance, or
imperfection, in
quaternions, or
rather in the state
to which it has been
hitherto unfolded,
whenever it becomes
or seems to become
necessary to have
recourse to x, y, z,
etc.

In a letter from
Tait to Cayley.

##### Hamilton, [Sir] William Rowan (1805-1865)

Who would not rather have the fame of Archimedes than that of his conqueror Marcellus?

In H. Eves Mathematical Circles Revisited, Boston: Prindle, Weber and Schmidt, 1971.

##### Halmos, Paul R.

To be a scholar of
mathematics you must
be born with talent,
insight,
concentration,
taste, luck, drive
and the ability to
visualize and guess.

I Want to Be a
Mathematician,
Washington: MAA
Spectrum, 1985.

##### Halmos, Paul R.

Don't just read it;
fight it! Ask your
own questions, look
for your own
examples, discover
your own proofs. Is
the hypothesis
necessary? Is the
converse true? What
happens in the
classical special
case? What about the
degenerate cases?
Where does the proof
use the hypothesis?

I Want to Be a
Mathematician,
Washington: MAA
Spectrum, 1985.

##### Halmos, Paul R.

The joy of suddenly
learning a former
secret and the joy
of suddenly
discovering a
hitherto unknown
truth are the same
to me -- both have
the flash of
enlightenment, the
almost incredibly
enhanced vision, and
the ecstasy and
euphoria of released
tension.

I Want to Be a
Mathematician,
Washington: MAA
Spectrum, 1985.

##### Halmos, Paul R.

[T]he source of all
great mathematics is
the special case,
the concrete
example. It is
frequent in
mathematics that
every instance of a
concept of seemingly
great generality is
in essence the same
as a small and
concrete special
case.

I Want to Be a
Mathematician,
Washington: MAA
Spectrum, 1985.

##### Halmos, Paul R.

I remember one
occasion when I
tried to add a
little seasoning to
a review, but I
wasn't allowed to.
The paper was by
Dorothy Maharam, and
it was a perfectly
sound contribution
to abstract measure
theory. The domains
of the underlying
measures were not
sets but elements of
more general Boolean
algebras, and their
range consisted not
of positive numbers
but of certain
abstract equivalence
classes. My proposed
first sentence was:
"The author
discusses valueless
measures in
pointless spaces."

I Want to Be a
Mathematician,
Washington: MAA
Spectrum, 1985, p.
120.

##### Halmos, Paul R.

[T]he student skit
at Christmas
contained a
plaintive line:
"Give us Master's
exams that our
faculty can pass, or
give us a faculty
that can pass our
Master's exams."

I Want to Be a
Mathematician,
Washington: MAA
Spectrum, 1985.